I'm an Illustrator Novice (I'm more experienced with Photoshop) but I need to create a vector version of our company logo.

The logo looks fine in Illustrator and if I export a png version it looks fine too:

However, when I save the .ai file as a PDF, I get this weird ghost text behind the other text and the shadows aren't as distinct (I created the shadow by duplicating layers with a small shadow so they would stack up, and I think some of those layers are getting shifted which causes the ghost text as well as the lighter shadow on the main text).